YES

Prover = TRS(tech=GUIDED_UNF_TRIPLES, nb_unfoldings=unlimited, unfold_variables=false, max_nb_coefficients=12, max_nb_unfolded_rules=-1, strategy=LEFTMOST_NE)

** BEGIN proof argument **
All the DP problems were proved finite.
As all the involved DP processors are sound,
the TRS under analysis terminates.
** END proof argument **

** BEGIN proof description **
## Searching for a generalized rewrite rule
(a rule whose right-hand side contains a variable
that does not occur in the left-hand side)...
No generalized rewrite rule found!

## Applying the DP framework...
## Round 1:
  ## DP problem: 
  Dependency pairs = [+^#(+(_0,_1),_2) -> +^#(_0,+(_1,_2)), +^#(+(_0,_1),_2) -> +^#(_1,_2), +^#(f(_0),f(_1)) -> +^#(_0,_1), +^#(f(_0),+(f(_1),_2)) -> +^#(f(+(_0,_1)),_2), +^#(f(_0),+(f(_1),_2)) -> +^#(_0,_1)]
  TRS = {+(+(_0,_1),_2) -> +(_0,+(_1,_2)), +(f(_0),f(_1)) -> f(+(_0,_1)), +(f(_0),+(f(_1),_2)) -> +(f(+(_0,_1)),_2)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {+(_0,_1):[_0 * _1], f(_0):[2 * _0], +^#(_0,_1):[_0 + _0 * _1]}
      for all instantiations of the variables with values greater than or equal to mu = 2.
  This DP problem is finite.

** END proof description **

Proof stopped at iteration 0
Number of unfolded rules generated by this proof = 0
Number of unfolded rules generated by all the parallel proofs = 28